This was a DAAD/British Council
funded collaborative research project: entitled
Uncertainty quantification in computer simulations of groundwater flow problems with
emphasis on contaminant transport
.
The project started in July 2006 and finished in September 2008.

Project Summary
Fluid flow and the transport of chemicals in porous media are modelled mathematically
using partial differential equations. In so-called deterministic modelling, inputs
such as material properties, boundary conditions and source terms are assumed to be known exactly.
However, simulations based on such over-simplifications cannot be used in practice to quantify
the probability of an unfavourable event such as, say, a chemical being transported at a lethal
level of concentration in groundwater. The permeability coefficients of rocks can never be
known at every point in space.
The so-called Stochastic Finite Element Method (SFEM) provides a framework for incorporating
statistical information about spatial variability in material parameters into computer simulations
of fluid flow problems so that more comprehensive information about the flow can be obtained.
A key feature is that the uncertain porosity coefficients in the governing flow equations are
represented as random fields. Consequently, the unknown quantities sought, e.g. fluid velocity,
concentrations of transported chemicals etc. are themselves random fields. Instead of performing
multiple deterministic simulations, one large calculation is performed, incorporating assumed
statistics of the random inputs. The output can be post-processed to determine probabilistic
information such as the expected concentration of a chemical in the groundwater at a
particular waste storage site.
The aim of this project is to develop codes to implement state of the art SFEM techniques and
perform simulations of contaminant transport in groundwater flow in porous media that
exhibit random spatial variability. In particular, we will focus on computational efficiency
and will develop fast, robust linear algebra techniques to solve the extremely large linear
systems of equations involved. We will validate our results against existing data and
compare our techniques with traditional deterministic methodologies based on multiple realisations.

Software
Our open source PIFISS
software for solving deterministic groundwater flow problems is freely available.
PIFISS is a MATLAB toolbox that is written in the IFISS
house-style, but using FEMLAB functions for grid generation.
The package has built-in algebraic multigrid and Krylov subspace solvers and appropriate
preconditioning strategies for each problem.